Monotremes
These primitive mammals (the only ones still living are the duckbill platypus and the echidna) lay eggs. They have all the attributes of mammals, but females lay leathery-shelled eggs somewhat like a reptile's. When the eggs hatch, the tiny, underdeveloped babies cling to the mother's furry belly and suck milk through pores in her skin.
Marsupials
Marsupials are more advanced in care of the young. Females have a pouch on the belly into which the blind and hairless young must climb after being born alive (not from an egg). Once they reach the pouch, they suckle milk from nipples there and stay there until they grow hair. Even after they can get around on their own and eat solid food, the pouch is still available to them for shelter from the elements and protection against predators. Most marsupials are found in Australia and New Zealand, but the U.S. has one: the Virginia opossum.
Placental Mammals
These mammals keep their unborn babies inside their bodies for a relatively long time. Females have a special internal organ, a uterus or womb, where the baby grows, connected to the mother while getting oxygen and nourishment through a placenta until it has a better chance of surviving in the outside world. Human babies stay in the womb for nine months; elephant babies stay in the womb for almost two years.
Other Types
Mammals can be typed in many ways. Some group them by things they do: do they walk, swim or fly? Others classify them according to what they eat: meat, vegetables or both? Still others divide them by physical characteristics: do they have teeth, what kind and how many? These are usually covered in the next major taxonomic division, the order, but the most basic division remains how they have babies.